Most of the dynamical systems that we have around us may be reasonably described in discrete time or continuous time and deterministic case or stochastic case. However, a large class of such physical systems may be modelled as hybrid ones; that is, to the continuous state variable, a discrete random variable called the mode, or regime, is appended. For instance, these may result from the abrupt phenomena such as component and interconnection failures, parameters shifting, tracking, and the time required to measure some of the variables at different stages. An interaction of these continuous and discrete dynamics will be appeared in response to discrete, instantaneous, events and in response to dynamics as described by differential or difference equations in time.

The overall aim of this special issue is to provide an up-to-date overview of the research directions and advanced methodologies in the hybrid dynamical systems. Of particular interest the papers in this special issue are devoted to the development of mathematical modeling, analysis, and control problems of hybrid systems, including Markovian jumping system, variable-structure systems with discontinuous dynamical systems, and switching systems. Topics include, but are not limited to:

• Modeling of hybrid systems including multitime-scale systems and hybrid automaton
• Stochastic analysis of hybrid systems with time delay effects
• Hybrid control and observer design
• Robust fault detection, diagnosis, and supervisory control
• Applications of hybrid systems to complex and large-scale systems

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